Seven metals were known to antiquity, copper, gold, iron, lead, mercury, silver, and tin. Each of these is discussed elsewhere. Of the ancient metals, copper may have been the most important, mercury the least. These seven metals either occur naturally in their metallic state (gold) or are easily extracted from their ores (mercury).
Early metalsmithing involves hammering and shaping soft metals as well as casting those with low melting points. Also early in history, metals are combined into alloys with new and different properties. The most important of these alloys is bronze, a combination of copper and tin. The Bronze Age is a distinct shift in technology and marks different years in different parts of the world. The Bronze Age starts around 3,300 BC in India, 2,500 BC in Europe, 2,000 BC in China, and before 1,000 BC in the Andes.
Other early alloys include some in which one or more of the constituent metals was never actually isolated. For example, early nickel alloys are known, and early brass was made from zinc ore rather than actual zinc. Additionally, many substances used from prehistoric times contain metals in their chemical makeup. The most obvious of these is salt, containing sodium, a metal not identified until the 19th century. Few of these substances exhibit metallic properties of their own and so should not be considered a direct part of the history of metals.
Wood or coal fires are sufficient for manipulating most of the ancient metals, but iron is different. Forced air from a bellows is required to obtain high enough temperatures to first smelt iron from its ore and then create steel. Many cultures never achieved an Iron Age, but we find evidence of iron smelting in India around 1400 B.C., Sub-Saharan Africa before 1200 B.C., and China around 500 B.C. Meteoric iron was recovered and shaped well before smelting was a possibility.

Medieval Metals

Very few additional metals were discovered until the industrial age. Platinum, bismuth, and zinc are among these intermediate discoveries. Most of the later developments in metallurgy until modern chemistry began involve hotter furnaces, purer smelting, and greater control of alloys.
A curious precursor to modern chemistry is the medieval activity known as alchemy. Alchemy has many philosophical aspects, but as a physical study it involves characterizing and manipulating the properties of substances. The seven known metals were elemental substances; interestingly, each metal was paired with one of the seven known planets.

☉

Sun

gold

☽

Moon

silver

☿

Mercury

mercury

♀

Venus

copper

♂

Mars

iron

♃

Jupiter

tin

♄

Saturn

lead

Alchemy began in the medieval Arab world (alchemy is an Arabic word) and was picked up by Western Europe. To modern eyes, the end goals of the alchemists seem misplaced – turn lead into gold, create the philosopher's stone, perfect an elixir of life. Nevertheless, alchemists developed techniques still used today.
Alchemists, particularly the early Islamic practitioners, created specialized laboratory equipment (and laboratories), repeated experiments, and a toolbox of procedures.
Each metal was considered to have a small number of fundamental attributes. For example, lead is "cold" and gold is "hot". To transform one into another, alchemists developed procedures such as distillation, filtration, and crystalization. The right combination of techniques would presumably turn "cold" lead into "hot" gold.
(Logically, turning gold into lead would be just as difficult as the reverse. Somehow, no efforts toward that end are attested to.)
The mystical aspects of alchemy fell somewhat out of fashion during the Renaissance and early industrial period. Nevertheless, famous figures such as Isaac Newton (1643-1727) spent a great deal of time on alchemical investigation. Not until the 18th century does alchemy substantially evolve into modern chemistry.

The Industrial Era

It is in the 18th century that chemistry and metallurgy become recognizable disciplines. A graph of the number of known metals (some dates are debatable) shows an explosion of knowledge after 1700.
The pioneers of chemistry of this period include Joseph Priestly (discovery of oxygen), Henry Cavendish (hydrogen), and Antoine Lavoisier (basic terminology and theory). Scientists such as Cavendish and Benjamin Franklin experimented with electricity, which would soon be a powerful tool for purifying metals. Also that century, James Watt perfected his steam engine for use in mining.
Many key inventions of this period involve the making of steel. For example, coke (treated charcoal) creates a hotter blast furnace while introducing fewer impurities. Toward the end of the Industrial Revolution, Henry Bessemer in 1855 invented the first cheap method of mass producing steel. By this time, iron and steel are incorporated into bridges, buildings, and railroads.
With respect to other metals, the Hall-Héroult process developed around 1888 turned aluminum from a curiosity into an affordable material. Copper required no breakthroughs to manufacture economically, but the growing demand for electrical wiring in the late 19th century coincided with westward expansion of the United States. Mines in Arizona, Montana, and elsewhere met this demand.

The Modern Era

In the 20th century, World War II, aviation, and electronics all drove research into metals and materials. Steel is still the most commonly used metal. As described in their individual sections, however, other major metals such as nickel and zinc have gained in importance because of their use with steel. Various metals are used either to plate steel vs. rust or to alloy with steel.
A new use for metals came with the proliferation of power transmission and then electronics. Previously, structural strength and malleability were the material properties of major interest. But, in the last 100 years, copper and aluminum have become desirable because they conduct electricity well. On a smaller scale, little-known metals such as gallium and indium make high-performance electronics possible.
Going forward, computer modeling allows metallurgy to proceed in a previously unknown way, predictively. The behavior of metal alloys can be predicted from calculations, where traditionally a foundry or laboratory would mix a sample and inspect it. The possibilities are open-ended.